where \(F^{\mu \nu }\)  is the electromagnetic field strength, \(\tilde{F}_{\mu \nu }\)  is its dual, \(a\)  denotes the ALP field whereas \(m\)  stands for the ALP mass As usual, natural Lorentz-Heaviside units with \(\hbar =c=1\)  are employed throughout.. According to the above view, it is assumed \(M \gg G_F^{- 1/2} \simeq 250 \, {\rm GeV}\) . On the other hand, it is supposed that \(m \ll G_F^{- 1/2} \simeq 250 \, {\rm GeV}\) . The standard Axion [1]} is the most well known example of ALP. As far as generic ALPs are concerned, the parameters \(M\)  and \(m\)  are to be regarded as independent.
